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LESSON 11–5

LESSON 11–5. Areas of Similar Triangles. Five-Minute Check (over Lesson 11–4) TEKS Then/Now Theorem 11.1: Areas of Similar Polygons Example 1: Find Areas of Similar Polygons Example 2: Use Areas of Similar Figures Example 3: Real-World Example: Scale Models. Lesson Menu.

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LESSON 11–5

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  1. LESSON 11–5 Areas of Similar Triangles

  2. Five-Minute Check (over Lesson 11–4) TEKS Then/Now Theorem 11.1: Areas of Similar Polygons Example 1: Find Areas of Similar Polygons Example 2: Use Areas of Similar Figures Example 3: Real-World Example: Scale Models Lesson Menu

  3. What is the area of a regular hexagon with side length of 8 centimeters? Round to the nearest tenth if necessary. A. 48 cm2 B. 144 cm2 C. 166.3 cm2 D. 182.4 cm2 5-Minute Check 1

  4. What is the area of a square with an apothem length of 14 inches? Round to the nearest tenth if necessary. A. 784 in2 B. 676 in2 C. 400 in2 D. 196 in2 5-Minute Check 2

  5. Find the area of the figure. Round to the nearest tenth if necessary. A. 120 units2 B. 114 units2 C. 108 units2 D. 96 units2 5-Minute Check 3

  6. Find the area of the figure. Round to the nearest tenth if necessary. A. 184 units2 B. 158.9 units2 C. 132.6 units2 D. 117.7 units2 5-Minute Check 4

  7. Find the area of the figure. A. 11 units2 B. 12 units2 C. 13 units2 D. 14 units2 5-Minute Check 5

  8. Find the area of a regular triangle with a side length of 18.6 meters. A. 346 m2 B. 299.6 m2 C. 173 m2 D. 149.8 m2 5-Minute Check 6

  9. Targeted TEKS G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. Mathematical Processes G.1(A), G.1(F) TEKS

  10. You used scale factors and proportions to solve problems involving the perimeters of similar figures. • Find areas of similar figures by using scale factors. • Find scale factors or missing measures given the areas of similar figures. Then/Now

  11. Concept

  12. 9 3 __ __ 6 2 The scale factor between PQRS and ABCD is or .So, the ratio of the areas is Find Areas of Similar Polygons If ABCD ~ PQRS and the area of ABCD is 48 square inches, find the area of PQRS. Example 1

  13. Find Areas of Similar Polygons Write a proportion. Multiply each side by 48. Simplify. Answer: So, the area of PQRS is 108 square inches. Example 1

  14. If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO. A. 180 ft2 B. 270 ft2 C. 360 ft2 D. 420 ft2 Example 1

  15. Use Areas of Similar Figures The area of ΔABC is 98 square inches. The area of ΔRTS is 50 square inches. If ΔABC ~ ΔRTS, find the scale factor from ΔABC to ΔRTS and the value of x. Let k be the scale factor between ΔABC and ΔRTS. Example 2

  16. So, the scale factor from ΔABC to ΔRTS isUse the scale factor to find the value of x. Use Areas of Similar Figures Theorem 11.1 Substitution Simplify. Take the positive square root of each side. Example 2

  17. Use Areas of Similar Figures The ratio of corresponding lengths of similar polygons is equal to the scale factor between the polygons. Substitution 7x = 14 ● 5 Cross Products Property. 7x = 70 Multiply. x = 10 Divide each side by 7. Answer: x = 10 Example 2

  18. CHECK Confirm that is equal to the scale factor. Use Areas of Similar Figures Example 2

  19. The area of ΔTUV is 72 square inches. The area ofΔNOP is 32 square inches. If ΔTUV ~ ΔNOP, use the scale factor from ΔTUV to ΔNOP to find the value of x. A. 3 inches B. 4 inches C. 6 inches D. 12 inches Example 2

  20. Changing Dimensions CRAFTS Jonathon has a banner that measures 15 feet by 6 feet. He makes two additional banners that measure 30 feet by 12 feet and 30 feet by 10 feet, respectively. Describe how the difference in dimensions affects the areas of the banners. Answer: The dimensions of the first banner increase proportionally by a scale factor of 2, so the area of the first banner is 4 times the area of the original banner. On the second banner, the width doubles and the length increases by about 1.67 so it is a non-proportional change. The area of the second banner increases by the product of the scale factors of each dimension, so the area is 3.34 times greater than the area of the original. Example 3

  21. MODELS The area of one hood of a car is 35 square feet. The area of the hood of a model is 6 square inches. If the car is 14 feet long, about how long is the model? A. 4.3 inches B. 5.8 inches C. 6.7 inches D. 7.2 inches Example 3

  22. LESSON 11–5 Areas of Similar Triangles

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